Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
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SIAM Journal on Computing
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ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Single machine precedence constrained scheduling is a vertex cover problem
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
Operations Research Letters
Scheduling with Precedence Constraints of Low Fractional Dimension
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the Approximability of Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
The feedback arc set problem with triangle inequality is a vertex cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Vertex cover in graphs with locally few colors
Information and Computation
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This paper investigates the relationship between the dimension theory of partial orders and the problem of scheduling precedence-constrained jobs on a single machine to minimize the weighted completion time. Surprisingly, we show that the vertex cover graph associated to the scheduling problem is exactly the graph of incomparable pairs defined in dimension theory. This equivalence gives new insights on the structure of the problem and allows us to benefit from known results in dimension theory. In particular, the vertex cover graph associated to the scheduling problem can be colored efficiently with at most k colors whenever the associated poset admits a polynomial time computable k-realizer. Based on this approach, we derive new and better approximation algorithms for special classes of precedence constraints, including convex bipartite and semi-orders, for which we give $(1+\frac{1}{3})$-approximation algorithms. Our technique also generalizes to a richer class of posets obtained by lexicographic sum.